Keeping crypto on an exchange means trusting that exchange to keep custody of your keys and stay solvent — convenient, but you don’t actually hold the keys.
A software wallet on your phone or computer gives you the keys, but they’re stored on a general-purpose device that can run other apps, browse the web, and potentially be compromised by malware.
A hardware wallet generates and stores keys inside an isolated secure element that never runs arbitrary software, and requires a physical confirmation for every transaction — the strongest common option for long-term, self-custodied holdings.